Fisheye Stereo Vision: Depth and Range Error

TL;DR

This work tackles the challenge of depth and range estimation in fisheye stereo by deriving closed-form expressions for $Delta Z$ and $Delta R$ that account for large-angle incidence. It contrasts the pinhole and fisheye projections, showing that while pinhole error scales with baseline foreshortening, fisheye error is amplified by the factor $(1+ tan^2 theta)$ due to angular-resolution degradation. The authors validate the analysis with a practical 4K fisheye stereo setup ($B = 1$ m) and demonstrate sub-4 cm range accuracy at 10 m within a wide angular range, while highlighting the benefits of real-time autocalibration for maintaining wide-baseline depth sensing. The results guide design choices for wide-field-of-view depth sensing, including baseline selection and calibration strategies to mitigate peripheral precision loss.

Abstract

This study derives analytical expressions for the depth and range error of fisheye stereo vision systems as a function of object distance, specifically accounting for accuracy at large angles.

Figures (2)

• Figure 1: Stereo vision cameras. The dashed light rays correspond to the pinhole camera model and the solid light rays correspond to the fisheye camera model. The depth and range errors are shown for both camera models.
• Figure 2: Range error for pinhole and fisheye camera plotted as a function of the angle of incidence. The depth, $Z$, is 10 m; focal length, $f$, is 1222.3 pixels; the baseline, $B$, is 1 meter; and the disparity error, $\Delta d$, is 0.2 pixels. This plot was generated from this publicly available notebook colab.